Data is becoming increasingly important in our highly digitised world. This is painfully apparent when you lose it. As the saying goes: You don't know what you've got until it's gone.
There are many strategies for backups and all of them have their positive and negative aspects.
Online
Online backup solutions are good because they are safe from natural disasters and theft that may occur at your office or home, but online accounts can be hacked and the service may potentially suffer from downtime due to failure of any systems involved including your internet connection. Even the most reliable online services fail ocassionally. Microsoft, Google, Dreamhost, etc. all suffered downtime at some point in time.
Also, online backups may take a very long time initially and may cost lot of bandwidth. Retrieval of data is also slow because you actually have to download the data from an off-site server.
Make sure when using online backup services to use a very hard to guess password that is totally different from all your other passwords, so if your other accounts are compromised it will not affect your backups.
Offline
Local backup solutions are good because they are quick to access when needed and relatively cheap as you only need to invest once in the hardware, which may last for years to come.
On the downside they are prone to the same environmental issues that may cause to lose data on your computer in the first place. If you have local backup it's a good idea to keep it in a fire-safe box in a different room from where you keep your Mac. If you happen to have a safe, keep it in there.
I had a friend who had his computer and his backups stolen all at once, so he had not much use having all his work meticulously backed up.